Cardinal Timothy Dolan of New York, president of the U.S. Conference of Catholic Bishops, has released a statement along with other archbishops declaring the Supreme Court's ruling on two major gay marriage cases as a "tragic day for marriage and our nation."

"The Supreme Court has dealt a profound injustice to the American people by striking down in part the federal Defense of Marriage Act. The Court got it wrong. The federal government ought to respect the truth that marriage is the union of one man and one woman, even where states fail to do so," read a joint statement by Dolan and Archbishop Salvatore Cordileone of San Francisco, chair of the U.S. bishops' Subcommittee for the Promotion and Defense of Marriage, released on the USCCB website after the Supreme Court decisions on Wednesday.

By striking down parts of DOMA, the Supreme Court now allows married same-sex couples to receive the same tax, health and retirement benefits that are available to married heterosexual couples. And by rejecting an appeal on an earlier court decision that overturned California's Proposition 8, the amendment that defined marriage as a union between a man and a woman, the Court also paved the way for gay marriage in the state.

The bishops' statement said that it is "unfortunate" that the Supreme Court did not uphold Proposition 8, arguing that the common good for everyone, especially children, "depends upon a society that strives to uphold the truth of marriage."

"The future of marriage and the well-being of our society hang in the balance," the statement continued.

"Marriage is the only institution that brings together a man and a woman for life, providing any child who comes from their union with the secure foundation of a mother and a father."

Dolan and Cordileone insisted that there is a very important difference between a man and a women, as well as fathers and mothers, and that people should work toward strengthening the traditional view of marriage, not redefining it.

"When Jesus taught about the meaning of marriage – the lifelong, exclusive union of husband and wife – he pointed back to 'the beginning' of God's creation of the human person as male and female (see Matthew 19). In the face of the customs and laws of his time, Jesus taught an unpopular truth that everyone could understand. The truth of marriage endures, and we will continue to boldly proclaim it with confidence and charity."

The gay marriage decisions on Wednesday proved popular among LGBT activists and a number of liberal politicians, including President Barack Obama, but many Conservative groups and Christians expressed their disappointment with the rulings.

Dolan has spoken out on gay rights issues before, affirming the Roman Catholic stance on traditional marriage, but insisted that the defense of marriage should not be reduced to an attack on gay people.

"And I admit, we haven't been too good at that. We try our darndest to make sure we're not an anti-anybody," the most senior Catholic cleric in America said in an interview earlier this year.

A March 2013 Pew Forum survey found that much like the rest of the American population, U.S. Catholics hold conflicting views on the issue of gay marriage.

Sixty-two percent of Catholics who responded to the poll said that same-sex marriage would violate their religious beliefs, compared to 35 percent who said that it would not. At the same time, however, 54 percent of Catholics also said they support legalized same-sex marriage.